Harry Daniels is a quality control engineer for the Specific Electric Corporation. Specific manufactures electric motors. One of the steps in the manufacturing process involves the use of an automatic milling machine to produce slots in the shafts of the motors. Each batch of shafts is tested, and all shafts that do not meet required dimensional tolerances are discarded. The milling machine must be readjusted at the beginning of each new batch because its cutter head wears slightly during production. Harry is assigned the job of forecasting how the size of a batch affects the number of defective shafts in the batch so that he can select the best batch size. He collects the data for the average batch size of 13 batches shown in Table P-13 and assigns you to analyze it.

a. Plot the data as a scatter diagram.
b. Fit a simple linear regression model.
c. Test for the significance of the slope coefficient.
d. Examine the residuals.
e. Develop a curvilinear model by fitting a simple linear regression model to some transformation of the independent variable.
f. Test for the significance of the slope coefficient of the transformed variable.
g. Examine the residuals.
h. Forecast the number of defectives for a batch size of 300.
i. Which of the models in parts b and e do you prefer?
j. Write Harry a memo summarizing your results.

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TABLE P-13 Number of Defectives Batch Size Batch 50 75 100 125 150 175 200 225 250 275 300 325 16 27 36 49 53 70 82 95 109 10 12 13